A topological data analysis based classifier

Kindelan, Rolando; Frías, José Ángel Garfias; Cerda, Mauricio; Hitschfeld, Nancy

doi:10.1007/s11634-023-00548-4

Cited by 1 publication

(1 citation statement)

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“…The same principle was used in [30] to obtain a new TDA-based semi-supervised learning method. A different mechanism for TDA-based classification was described in [31,32] as a refinement of nearest neighbour classifiers by exploiting the local structure of Vietoris-Rips simplicial complexes associated with a data cloud.…”

Section: Introductionmentioning

confidence: 99%

A topological classifier to characterize brain states: When shape matters more than variance

Ferrà,

Cecchini,

Nobbe Fisas

et al. 2023

PLoS ONE

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Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is more important, about the phenomena being characterized by the given datasets. By contrast, topological data analysis (TDA) is devoted to study the shape of data clouds by means of persistence descriptors and provides a quantitative characterization of specific topological features of the dataset under scrutiny. Here we introduce a novel TDA-based classifier that works on the principle of assessing quantifiable changes on topological metrics caused by the addition of new input to a subset of data. We used this classifier with a high-dimensional electro-encephalographic (EEG) dataset recorded from eleven participants during a previous decision-making experiment in which three motivational states were induced through a manipulation of social pressure. We calculated silhouettes from persistence diagrams associated with each motivated state with a ready-made band-pass filtered version of these signals, and classified unlabeled signals according to their impact on each reference silhouette. Our results show that in addition to providing accuracies within the range of those of a nearest neighbour classifier, the TDA classifier provides formal intuition of the structure of the dataset as well as an estimate of its intrinsic dimension. Towards this end, we incorporated variance-based dimensionality reduction methods to our dataset and found that in most cases the accuracy of our TDA classifier remains essentially invariant beyond a certain dimension.

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Section: Introductionmentioning

confidence: 99%